Romney was backed by 29 percent of Republican voters in the telephone poll conducted February 2-6, down from 30 percent in a survey in early January.
The former Massachusetts governor's three rivals in the race to oppose Democratic President Barack Obama in November were in a virtual tie for second, the poll showed. The gaps between the three were within the poll's margin of error.
Texas Congressman Ron Paul's support grew by 5 percentage points to 21 percent, moving him into second place and ahead of former House of Representatives speaker Newt Gingrich, whose support slipped to 19 percent from 20 percent.
Support for former Pennsylvania Senator Rick Santorum also rose by 5 points to reach 18 percent, putting him just behind Gingrich, according to the poll.
The results suggest Romney - despite his vast advantages in organization, fundraising and momentum after victories in New Hampshire, Florida and Nevada - still has many doubters among Republicans nationwide.
"He still hasn't really convinced all the Republicans across the country that he's the guy to get behind," said Chris Jackson, research director for Ipsos public affairs.
The Reuters/Ipsos poll also showed Obama's approval rating ticking upward during the past month, a period in which favorable reports on the economy seem to have given his re-election effort some momentum.
Obama's approval rating in the new poll is 48 percent, up from 47 percent in January. His disapproval rating is higher, though: 49 percent, unchanged from last month.
Many conservatives have worried Romney is not sufficiently conservative to be the Republican nominee to face Obama in the November 6 elections.
Gingrich and Santorum have each had shining moments during the state-by-state race for the Republican nomination, while Paul has shown the ability to consistently attract a core of loyal supporters.
Santorum won the Iowa caucuses on January 3 by a razor-thin margin over Romney, and Gingrich shocked Romney with a 12-point victory in South Carolina on January 21.
For the most part, however, the campaign has been dominated by Romney - and punctuated by attacks on Gingrich's character by Romney's campaign and an independent "Super PAC" that supports the former Massachusetts governor.
So the Republican race has been a contest with a clear frontrunner who hasn't yet been able to rally some of the most conservative members of the party.
"None of (Romney's rivals) has really managed to build up momentum to get to Romney's level," Jackson said.
The telephone poll of 1,033 adults included 881 registered voters, of whom 503 were Democrats, 405 Republicans and 125 independents.
The margin of error was plus or minus 3.1 percentage points for all respondents; 3.3 points for registered voters; 4.4 points for Democrats; 4.9 points for Republicans; and 9.6 points for independents.